On (m,n)-ideals of Left Almost Semigroups

Authors

  • Waqar Khan
  • Faisal Yousafzai University of Science and Technology of China, Hefei, China
  • Madad Khan

Keywords:

LA-semigroups, left invertive law, left identity and (m, n)-ideals

Abstract

In this paper, we study (m,n)-ideals of an LA-semigroup in detail. We charactrize (0,2)-ideals of an LA-semigroup S and prove that A is a (0,2)-ideal of S if and only if A is a left ideal of some left ideal of S. We also show that an LA-semigroup S is 0-(0,2)-bisimple if and only if S is right 0-simple. Furthermore we study 0-minimal (m,n)-ideals in an LA-semigroup S and prove that if R (L) is a 0-minimal right (left) ideal of S, then either R^{m}Lâ¿={0} or R^{m}Lâ¿ is a 0-minimal (m,n)-ideal of S for m,n≥3. Finally we discuss (m,n)-ideals in an (m,n)-regular LA-semigroup S and show that S is (0,1)-regular if and only if L=SL where L is a (0,1)-ideal of S.

Downloads

Published

2016-07-02

Issue

Vol. 9 No. 3: (July 2016)

Section

Differential Equations

License

Upon acceptance of an article by the European Journal of Pure and Applied Mathematics, the author(s) retain the copyright to the article. However, by submitting your work, you agree that the article will be published under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). This license allows others to copy, distribute, and adapt your work, provided proper attribution is given to the original author(s) and source. However, the work cannot be used for commercial purposes.

By agreeing to this statement, you acknowledge that:

  • You retain full copyright over your work.
  • The European Journal of Pure and Applied Mathematics will publish your work under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).
  • This license allows others to use and share your work for non-commercial purposes, provided they give appropriate credit to the original author(s) and source.

How to Cite

On (m,n)-ideals of Left Almost Semigroups. (2016). European Journal of Pure and Applied Mathematics, 9(3), 277-291. https://www.ejpam.com/index.php/ejpam/article/view/2231